Vibration control of laminated cylindrical panel with optimal piezoelectric patch

In this research, control of vibration in multilayered cylindrical panel with piezoelectric patch, under dynamic load is investigated, for the first time. The finite element method is used to solve the dynamic equations of the structure, which is based on first-order shear deformation theory, and equivalent single layer models with different rotations for the substrate and the piezoelectric patch is developed. The governing equations are obtained by using the Hamilton’s principle of virtual work, are discretized over the mid-plane, by using eight node shell element, leading into the matrix system of equations. The maximum controllability criterion is used for finding the optimal size and location of piezo-patch. According to the used control law, the applied voltage on the piezo-patch is proportional to the radial velocity component at the point, where the sensor is installed. In order to evaluate the performance of the formulation and finite element model, the natural frequencies obtained for the substrate laminated panel are compared with those in the literature. Then, having the dynamics of the optimal system, the frequency response for open and closed loop controls are studied. Finally, the effects of controller gain values and dimensions of panel and patch on the time response and damping rate of vibrations are illustrated.